CN108200522A - A kind of change regularization ratio normalization sub-band adaptive filtering method - Google Patents
A kind of change regularization ratio normalization sub-band adaptive filtering method Download PDFInfo
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Abstract
The invention discloses a kind of change regularization ratio normalization sub-band adaptive filtering methods, hearing aid feedback control system based on normalization sub-band adaptive filtering algorithm, based on ratio adaptive technique and become regularization parameter variation, zygote band adaptive filter algorithm updates sef-adapting filter；In order to further improve the performance of adaptive filter algorithm, the present invention is based on input signal, mean square error and estimating system noise energies, principle is declined by mean-squared departure maximum, updates regularization parameter, the method for foring the parameter update sub-band adaptive filtering for becoming regularization ratio；This method is applied in the audiofeedback system of hearing aid, better acoustic feedback inhibition can be obtained, lower steady misadjustment and faster convergence rate can be obtained.
Description
Technical Field
The invention relates to the field of signal processing, in particular to a regularization proportion normalization subband self-adaptive filtering method.
Background
At present, the adaptive filtering algorithm has various applications in life and production, such as system identification, interference prediction, adaptive equalization cancellation, and the like. The existence of the acoustic feedback phenomenon in the hearing aid brings great trouble to many hearing loss patients, and seriously influences the daily life of the hearing loss patients. Many adaptive filtering algorithm-based (AFC) methods are used to solve such problems, and normalized least mean square error (NLMS) has been widely used, and is often used to solve the Acoustic echo phenomenon due to its robustness and simple computation. However, when the input signal is a speech signal with strong correlation, the convergence speed of the algorithm is slow, the performance is poor, and the scene with high requirement on speech enhancement accuracy cannot be met. To overcome these drawbacks, Lee and Gan propose a new subband adaptive filtering structure by decomposing the full-band input signal into several subband signals that are very close to white noise signals. Therefore, for signals with strong correlation, the subband adaptive filtering algorithm shows a faster convergence rate, and the computational complexity is similar to that of the NLMS algorithm.
Considering networks, acoustic echo cancellation, and acoustic feedback cancellation in hearing aids, where sparsity is a key contributing factor, a normalized subband adaptive filtering algorithm may be applied in combination with a proportional adaptive technique to acoustic feedback suppression. The proportional adaptation technique can handle sparse environments, and the subband adaptive filtering technique can greatly improve the convergence condition under colored signals. Both of these approaches have been integrated into a single adaptive filtering algorithm in research to improve the performance of adaptive filters in many applications.
Similar to the NLMS algorithm, the regularization factor plays a crucial role in the subband adaptive filtering algorithm, in addition to the step factor affecting the performance of the algorithm. The stability of the subband adaptive filtering algorithm and the quality of the convergence condition depend on the value of the regularization factor. The regularization factor is a positive constant that is added to the squared euclidean norm of the input signal to solve the numerical problem when the power of the input signal is near zero.
By adjusting the regularization factor, the contradiction between the convergence rate and the steady-state imbalance of the relevant adaptive filtering algorithm can be solved. In the document, NI and the like solve the contradiction between convergence speed and steady state imbalance in the normalized subband adaptive filtering algorithm by utilizing a mean square deviation maximum descending principle through variable regularization parameters; in the document NI J. improved normalized sub-band adaptive filter [ J ]. Electronics Letters,2012,48(6): 320-. In the document YU Y, ZHAO H, Chen B.A new normalized sub-band-and adaptive filter adaptive step [ J ] Birkhauser Boston Inc.2016, (4) 1407-1418 ], an improved variable-step normalized sub-band adaptive filtering algorithm is provided, and a step parameter is adjusted by introducing an iterative contraction technique to minimize the prior error on each sub-band step, so that a lower steady-state detuning amount is displayed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a regularization proportion normalization subband self-adaptive filtering method which can ensure higher convergence speed and can keep lower detuning amount.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a normalization proportion normalization subband self-adaptive filtering method is a hearing aid feedback suppression system based on a normalization subband self-adaptive filtering algorithm, wherein the hearing aid feedback suppression system comprises an analysis filter bank and a synthesis filter bank and is used for respectively decomposing a microphone signal and a loudspeaker signal and generating corresponding subband signals; the system also comprises a group of adaptive filter banks which process the sub-band signals and have the same coefficient; the adaptive filter bank comprises a plurality of sub-band adaptive filters, and the coefficient of each sub-band adaptive filter is updated by updating the regularization factor of each sub-band adaptive filter.
Preferably, the updating of the coefficients of the subband adaptive filter is realized by a subband adaptive filtering algorithm with the following proportion, and the expression is:
wherein w (k) represents the coefficients of the subband adaptive filter; μ represents a variable step factor, and has a value of 1; u. ofi(k) An output signal representing the ith sub-band; e.g. of the typei,D(k) An error signal representing the ith subband; k represents the number of iterations and,representing the last update;representing the last coefficient of the subband adaptive filter; n represents the number of subband filters;representing a regularization factor.
Preferably, a diagonal matrix q (k) ═ diag [ g ] is introduced0(k),g1(k),...,gN-1(k)]The above algorithm is expressed as:
the elements in the diagonal matrix q (k) may be defined as:
wherein M represents the acoustic feedback path length; epsilon is a constant; i | · | purple wind1Represents a vector l1Norm operator of-1 ≦ α ≦ 1.
Preferably, the method for updating the regularization factor of each subband adaptive filter is as follows:
a. will be provided withWritten in matrix form as follows:
wherein U (k) ═ u0,D(k) u1,D(k)… uN-1,D(k)]Is a subband input signal; e.g. of the typeD(k)＝[e0,D(k) e1,D(k) … eN-1,D(k)]TIs a subband error signal; Γ (k) ═ Φ (k) + Δ (k), Φ (k) ═ diag [ | | u [ ]0(k)||2||u1(k)||2… ||uN-1(k)||2]Δ(k)＝diag[δ0(k) δ1(k) … δN-1(k)]；
b. Defining an error vector e for a normalized subband adaptive filtering algorithmD(k) A priori error vector eaAnd the mean square deviation m (k) are respectively as follows:
wherein wo ═ wo,0wo,1… wo,k-1]Representing acoustic feedback pathsCoefficient of (2), vector dD(k) For the subband desired signal, vD(k) Defining the ith sub-band system noise as v for the sub-band system noise vectori,D(k) From this, the difference between the mean square deviations at kN times can be derived:
minimizing the formula according to the maximum descending principle of mean square deviation, and pairing two sides of the formula with deltai(k) Calculating a deviation guide, orderThe updated formula for the regularization factor is as follows:
wherein,is the variance power of the input signal;is the power of the subband error signal;is the system noise power; e [. C]Represents a mathematical expectation;
c. order toi is 0,1, …, N-1; the regularization factor is updated to:
wherein,is to update deltai(k) Step-size factor of time, contributing to the convergence of regularization factor, LkA positive number with a value greater than 0; deltamax(k) Is the maximum allowable regularization factor;indicating the next update;
d. obtaining variance power of input signalAnd power of sub-band error signalThe following were used:
wherein β is a forgetting factor, and the value is β ═ 0.995;
e. estimating and obtaining system noise power when the sub-band adaptive filter is in static state
The invention has the following beneficial effects:
(1) the regularization parameter is updated based on an input signal, a mean square error and an estimated system noise energy through a mean square deviation maximum descent principle; the method is applied to a hearing aid feedback suppression system with a long echo path and a short echo path, so that acoustic feedback signals can be better removed, and faster convergence speed and lower detuning amount can be obtained;
(2) the invention has good sound feedback inhibition effect under various conditions that the input signal is white noise, colored signal and complex voice signal, good tracking performance removes sound feedback, and faster convergence speed and lower detuning amount can be obtained;
(3) the regularization proportion normalization subband adaptive filtering method provided by the invention has the characteristics of low computational complexity and good robustness, and is suitable for the fields of echo cancellation, system identification, adaptive interference cancellation and the like.
The present invention will be described in further detail with reference to the drawings and embodiments, but the regularization ratio normalization subband adaptive filtering method of the present invention is not limited to the embodiments.
Drawings
Fig. 1 is a diagram of a hearing aid feedback suppression system based on a normalized subband adaptive filtering algorithm according to an embodiment of the present invention;
FIG. 2 shows the acoustic feedback path conditions of an embodiment of the present invention, where FIG. 2(a) shows a short echo path and FIG. 2(b) shows a long echo path;
fig. 3 is a graph illustrating comparison of the performance of feedback suppression by the white noise algorithm when the input signal is in accordance with various methods of the present invention, where fig. 3(a) is a graph illustrating comparison of the performance of feedback suppression by a short echo path, and fig. 3(b) is a graph illustrating comparison of the performance of feedback suppression by a long echo path;
FIG. 4 is a comparison of algorithm tracking performance for white noise and colored signals in the case of input signals, FIG. 4(a) for a white noise input signal and FIG. 4(b) for a colored signal, according to various embodiments of the present invention;
FIG. 5 is a graph illustrating comparison of acoustic feedback suppression performance of various methods according to embodiments of the present invention in the case of speech signal input; fig. 5(a) is a graph comparing the acoustic feedback suppression performance in the short echo path, and fig. 5(b) is a graph comparing the acoustic feedback suppression performance in the long echo path.
Detailed Description
The invention is further described below by means of specific embodiments.
A regularization proportion normalization subband self-adaptive filtering method comprises the following steps:
1) FIG. 1 illustrates the acoustic feedback suppression of a digital hearing aid based on a normalized subband adaptive filtering algorithm, whereinIncluding input signals for desired signalsAnd echo feedback signalInput signalIncluding real speech signalsAnd system noise signalBecause, in the elimination of the acoustic feedback, becauseIs the true speech signal that needs to be amplified and therefore can be first not calculated, the desired signal can be expressed as:
wherein, wo＝[wo,0wo,1… wo,k-1]Representing acoustic feedback pathsA coefficient vector of (a); signals picked up from microphonesMinus is made byBy passingThe feedback signal estimation valueThe signal without acoustic feedback can be obtainedAnd output by the speaker through forward gain amplification. Let N be the number of subband filters and L be the length of the analysis filter,for the number of iterations to be performed,in the structure, the subband filter bank is a cosine modulation filter bank, and the accuracy of a reconstructed signal is ensured. Microphone signalAnd loudspeaker signalRespectively pass through analysis filter bankDecompose to generate the correspondingOf the subband signal di(n) and ui(n), subband signal ui(n) passing through an adaptive filterPost-generation of subband output signal yi(N) and then N-fold down-sampling the sub-band signal to generate a sub-band signalAnd are filter banks having the same coefficients, with subband error signals ofSynthesizing full band error signal e by synthesis filterD(k) In that respect In which the same full-band adaptive filter is used for each sub-band, the filterThe coefficients of the coefficients are where N is the acoustic feedback path length. Then it is firstThe sub-band error signals are defined as:
wherein,based on the minimum disturbance principle, Lee and Gan adopt constraint equations as formulas (3) and (4), and a normalized subband adaptive filtering algorithm is derived through an optimization method:
the normalized sub-band adaptive filtering algorithm updating formula can be obtained by utilizing Lagrange to solve:
where μ is the step factor and δ is the regularization parameter.
2) The normalized subband adaptive filter algorithm derived from equation (5) changes δ in the equation to a regularization factor δ that varies with the time series kNi(k) And the step factor μ is 1, the regularized subband adaptive filtering algorithm can be written as:
the idea of the scale-up is to assign a separate step size to each tap weight based on the value of the last estimated tap weight. It uses proportionally larger steps for tap weights with larger values and reduces the steps to near zero (or not update) for smaller tap weights, resulting in faster convergence when the unknown system to be identified has sparse impulse responses. Whereas a sparse impulse response is one with a small percentage of components, with significant amplitude, while the rest is small or close to zero.
First, a diagonal matrix is introduced: q (k) ═ diag [ g0(k),g1(k),...,gN-1(k)]The elements in the diagonal control matrix may be defined as:
wherein epsilon is a small constant, | · |. non-woven phosphor1Is a representation vector l1Where-1 ≦ α ≦ 1, and in practice α is 0 or-0.5 is a suitable value, the proportional subband adaptive filter algorithm (PNSAF) may be expressed as:
3) writing the above formula into a matrix form, to obtain:
wherein U (k) ═ u0,D(k) u1,D(k) … uN-1,D(k)]Is a subband input signal; e.g. of the typeD(k)＝[e0,D(k)e1,D(k) … eN-1,D(k)]TIs the subband error signal. Where Γ (k) ═ Φ (k) + Δ (k), Φ (k) ═ diag [ | | u [ ]0(k)||2||u1(k)||2… ||uN-1(k)||2]Δ(k)＝diag[δ0(k) δ1(k) … δN-1(k)]. Defining an error vector e for a normalized subband adaptive filtering algorithmD(k) A priori error vector eaAnd the mean square deviation m (k) are respectively as follows:
wherein, wo＝[wo,0wo,1… wo,k-1]Representing acoustic feedback pathsCoefficient of (2), vector dD(k) For the subband desired signal, vD(k) For the subband system noise vector, defineSubband system noise vi,D(k) From this, the difference between the mean square deviations at kN times can be derived:
the above equation is minimized according to the mean square deviation maximum descent principle. Paired upper type two-side pair deltai(k) Calculating a deviation guide, orderObtaining an updated formula of the regularization:
whereinIs the power of the variance of the input signal,is the power of the sub-band error signal,is the system noise power.
4) The new proportional NSAF regularization update formula can be expressed as the following formula, and in the acoustic feedback normalization subband adaptive filtering algorithm, the parameter for updating the regularization factor is equivalent to the value for effectively reducing the variable step size parameter, so that the value μ of the step size is made to be 1, and the value of the regularization factor is adjusted, which is helpful for accelerating the convergence speed of the algorithm and reducing the steady-state detuning amount. Order toi is 0,1, …, N-1. The regularization parameter of the new scaled normalized subband adaptive filtering algorithm may be updated to be:
wherein,is to update deltai(k) Step-size factor of time, contributing to the convergence of regularization factor, LkA positive number greater than 0.
5) For theThe value of (d) can be calculated according to the following equation:
β in the above formula is a forgetting factor, which is β -0.995, andthe estimation can be obtained by estimating when the adaptive filter is in a static state, and the specific implementation can be referred to in the literature "YU Y, ZHAO H, Chen B.A new normalized ubba-nd adaptive filter with adaptive variable step [ J].Birkhauser Boston Inc.2016,35(4):1407-1418.”。
In modern digital hearing aids there is an increasing trend towards miniaturization and the study of the de-voicing feedback path must also take into account room reflections and the acoustic echo environment within the hearing aid ear canal. Referring to fig. 2, the experiment simulated two acoustic echo paths required: a. referring to fig. 2(a), a short echo path, namely, an echo path from a microphone to a loudspeaker is shown; b. referring to fig. 2(b), a long echo path, i.e. an echo path including room reflections, is shown. The sampling frequency is 8kHz for the unit impulse response of the echo path shown in figure 2.
Experiment-algorithm Performance in white noise Environment
Referring to fig. 3, in two different acoustic feedback paths (where fig. 3(a) is a graph comparing the acoustic feedback suppression performance in the short echo path and fig. 3(b) is a graph comparing the acoustic feedback suppression performance in the long echo path), the input signal is a gaussian random white noise sequence, the ambient noise v (n) is zero in mean, and the variance isThe proposed algorithm is based on comparison with several related subband adaptive filtering methods, as shown in fig. 3, the steady state detuning amount of the proposed algorithm is lower than that of other subband adaptive filtering algorithms, the convergence speed is much lower in the short echo path and faster in the long echo path than in the other algorithms, wherein the Improved Normalized Subband Adaptive Filtering (INSAF) algorithm results in poor convergence due to the use of the mean value of the past time coefficients when updating the filter coefficients, the number of subbands is set to N16, the related algorithm parameters are set to μ 1, Q1000 in Normalized Subband Adaptive Filtering (NSAF) and PNSAF algorithm, the step size is μ 0.2 in INSAF algorithm, P2 in INSAF algorithm, μ 1, Q631000 in normalized subband adaptive filtering algorithm (VR-NSAF), the step size is set to λ 24, N862, N kM., N36 β, and the step size is set to λ 24, N3, N3, Nk＝8，
Experimental two-algorithm tracking performance comparison
Tracking performance is a very important issue in adaptive algorithms. In applications such as acoustic feedback cancellation, the adaptive filter must track quickly because the impulse response is not very stable. Referring to fig. 4, white gaussian and white noise are passed through an AR first-order model g (z) 1/(1-0.9 z), respectively-1) And all algorithm parameters are set in one time of experiment, and the algorithm performance is compared when the system is subjected to mutation. Fig. 4(a) shows that the proposed algorithm converges quickly and has a lower amount of steady-state detuning when white noise is input. In fig. 4(b), when the AR model is input, the steady-state detuning amount of each algorithm is the same as gaussian white noise, when the system suddenly changes, the VR-NSAF convergence performance is poor, and for the INSAF algorithm, the convergence performance cannot be reflected because the average value of the coefficients at the past time is used when the filter coefficients are updated. The proposed algorithm has faster convergence speed in both cases and lower steady-state detuning amount.
Experimental three-Speech input Algorithm Performance
The parameters are set as follows, the step size is 0.5 in NSAF and PNSAF algorithm, the step size is 0.2 in INSAF algorithm, and P is 2 in INSAF algorithm, the step size is 1 in VR-NSAF algorithm, Q is 1000 in VSS-NSAF algorithm, the step size is 4 in VSS-NSAF algorithm, and the step size is 1-N/kM. in algorithm proposed by mu is 1, β is 0.995, L is 1-N/kM.k＝8，As shown in fig. 5, in the various subband adaptive filtering algorithms, the convergence rate and the steady-state detuning amount are similar to those in the input of gaussian white noise. In the short echo path, the PNSAF algorithm fluctuates greatly, and since the NSAF algorithm is added to the proportional adaptive algorithm, the proportional coefficient cannot guarantee a good convergence rate when a low misalignment amount is obtained when the step length is allocated. Therefore, the normalized subband adaptive filtering algorithm with the regularization ratio can still keep lower steady-state offset and faster receiving under the environment that speech is taken as an input signalAnd (4) the convergence speed.
The method is based on input signals, mean square error and estimated system noise energy, and updates regularization parameters while combining a subband adaptive filtering algorithm in a proportional adaptive technology. The regularization parameter is not limited to a small positive number during the update, but rather to a large positive number during the steady state phase. By adjusting the regularization parameters, the regularized proportional subband self-adaptive filtering method is invented. Experimental simulation shows that the algorithm is applied to an acoustic feedback system of a hearing aid, and a better acoustic feedback elimination effect can be achieved. The algorithm can obtain lower steady-state detuning amount and faster convergence speed under the conditions of white noise input, colored signals and real voice signals.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the present invention, and these modifications should also be construed as the protection scope of the present invention.
Claims (4)
1. A normalization proportion normalization subband self-adaptive filtering method is a hearing aid feedback suppression system based on a normalization subband self-adaptive filtering algorithm, wherein the hearing aid feedback suppression system comprises an analysis filter bank and a synthesis filter bank and is used for respectively decomposing a microphone signal and a loudspeaker signal and generating corresponding subband signals; the system also comprises a group of adaptive filter banks which process the sub-band signals and have the same coefficient; the adaptive filter bank includes a plurality of subband adaptive filters, characterized in that: and updating the coefficient of each sub-band adaptive filter by updating the regularization factor of each sub-band adaptive filter.
2. The method for removing acoustic feedback based on variable-step normalized subband adaptive filtering according to claim 1, wherein the updating of the coefficients of the subband adaptive filter is realized by a subband adaptive filtering algorithm with the following ratio, and the expression is:
wherein w (k) represents the coefficients of the subband adaptive filter; μ represents a variable step factor, and has a value of 1; u. ofi(k) An output signal representing the ith sub-band; e.g. of the typei,D(k) An error signal representing the ith subband; k represents the number of iterations, and k +1 represents the last update; w (k +1) represents the last coefficient of the subband adaptive filter; n represents the number of subband filters; deltai(k) Representing a regularization factor.
3. The method of claim 1, wherein a diagonal matrix q (k) -diag [ g ] is introduced0(k),g1(k),...,gN-1(k)]The above algorithm is expressed as:
the elements in the diagonal matrix q (k) may be defined as:
wherein M represents the acoustic feedback path length; epsilon is a constant; i | · | purple wind1Represents a vector l1Norm operator of-1 ≦ α ≦ 1.
4. The method of claim 3, wherein the method of updating the regularization factor of each subband adaptive filter is as follows:
a. will be provided withWritten in matrix form as follows:
wherein U (k) ═ u0,D(k) u1,D(k) … uN-1,D(k)]Is a subband input signal; e.g. of the typeD(k)＝[e0,D(k) e1,D(k)… eN-1,D(k)]TIs a subband error signal; Γ (k) ═ Φ (k) + Δ (k), Φ (k) ═ diag [ | | u [ ]0(k)||2||u1(k)||2…||uN-1(k)||2，Δ(k)＝diag[δ0(k) δ1(k) … δN-1(k)]；
b. Defining an error vector e for a normalized subband adaptive filtering algorithmD(k) A priori error vector eaAnd the mean square deviation m (k) are respectively as follows:
wherein, wo＝[wo,0wo,1… wo,k-1]Representing an acoustic feedback path woCoefficient of (z), vector dD(k) For the subband desired signal, vD(k) Defining the ith subband system for the subband system noise vectorNoise is vi,D(k) From this, the difference between the mean square deviations at kN times can be derived:
minimizing the formula according to the maximum descending principle of mean square deviation, and pairing two sides of the formula with deltai(k) Calculating a deviation guide, orderThe updated formula for the regularization factor is as follows:
wherein,is the variance power of the input signal;is the power of the subband error signal;is the system noise power; e [. C]Represents a mathematical expectation;
c. order toThe regularization factor is updated to:
wherein,is to update deltai(k) Step-size factor of time, contributing to the convergence of regularization factor, LkPositive number with value greater than 0；δmax(k) Is the maximum allowable regularization factor; k-1 represents the next update;
d. obtaining variance power of input signalAnd power of sub-band error signalThe following were used:
wherein β is a forgetting factor, and the value is β ═ 0.995;
e. obtaining the System noise Power by the method shown in the estimation when the subband adaptive Filter is in the static State
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